Walk in areas are generally private land that the game and fish pays a fee to receive public access to (that is what your "access yes" donation goes towards). I am unaware if that counts as "private" in the eyes of the G&F, I would call the local game warden and ask.
Your type 2 allows "any" antelope. I know that you won't want to, but if you get desperate and your about to eat tag soup because you can't get permission to harvest a buck without paying a large trespass fee, ask landowners if you can harvest a doe pronghorn on their land, and they are more likely to allow you to do so. A buddy of mine got permission to harvest doe pronghorn this last year in area 102. That way, you will at least get some pronghorn meat, and get to hunt.
Otherwise, practice your hat in hand speech, because your likely going to do it many, many times. I have hunted up there before and done that song and dance, it is even somewhat challenging getting permission to harvest doe whitetail deer at times.
Again, good luck. hopefully you will find a kind soul up there. Those areas have high draw odds for good reason. They are always my 3rd choice as a resident, I may not be able to get a good buck, but I always get a tag and at least a small opportunity to harvest a buck.